1. Field of the Invention
The present invention relates to a control system for driving synchronous motors at speeds higher than rated speeds.
2. Description of the Prior Art
Synchronous motors have heretofore been used in a wide field of applications and, in most cases, are operated at constant speed utilizing their constant-speed characteristics. Synchronous motors excited with permanent magnets, however, are often driven at varying speeds, and are sometimes operated at speeds greater than the rated speeds.
To run the synchronous motor at speeds faster than the rated speed, however, it is necessary to increase not only the frequency of the power supply but also to increase the power-supply voltage in view of its characteristics.
This is illustrated below. FIG. 1 is a vector diagram showing the relationship between the voltage and the current when a general salient-pole synchronous motor is operated. From FIG. 1, the following relationship holds true: EQU V=E+Iqr+Idr+jIdXd+jIqXq (1)
where V denotes a terminal voltage V, E denotes an induced electromotive force [volts], Id and Iq denote a direct-axis current component [amps] and a quadrature-axis current component [amps] in the armature current I, Xd and Xq denote a direct-axis reactance [ohms] and a quadrature-axis reactance [ohms], and r denotes an armature resistance.
If now the angular velocity of the rotor is given by .omega.r [rad/s], the induced electromotive force E, the direct-axis reactance Xd and the quadrature-axis reactance Xq in the above equation (1) are given by, EQU E=K.sub.E .multidot..omega.r (2a) EQU Xd=K.sub.d .multidot..omega.r (2b) EQU Xq=K.sub.q .multidot..omega.r (2c)
where K.sub.E, K.sub.d and K.sub.q denote coefficients.
Here, the induced electromotive force is denoted by E.sub.1 [volts], the direct-axis reactance is denoted by Xd.sub.1 [ohms] and the quadrature-axis reactance is denoted by Xq.sub.1 [ohms] when the synchronous motor is running at a rated speed .omega.n [rad/s]. Then, if the induced electromotive force is denoted by E.sub.2 [volts], the direct-axis reactance by Xd.sub.2 [ohms] and the quadrature-axis reactance by Xq.sub.2 [ohms] with the angular velocity of the synchronous motor being changed to 2 .omega.n [rad/s], the following relations hold true from the above relations (2a), (2b), and (2c): EQU E.sub.2 =2E.sub.1 ( 3a) EQU Xd.sub.2 =2Xd.sub.1 ( 3b) EQU Xq.sub.2 =2Xq.sub.1 ( 3c)
Further, from the equation (1) and referring to FIG. 1, the magnitude V [volts] or vector V is given by, ##EQU1##
Therefore, if the terminal voltage, direct-axis current component and quadrature-axis current component are denoted by V.sub.1 [volts], Id.sub.1 [amps] and Iq.sub.1 [amps] when the synchronous motor is running at the angular velocity .omega.n [rad/s], and if the above-mentioned quantities are denoted by V.sub.2 [volts], Id.sub.2 [amps] and Iq.sub.2 [amps] when the synchronous motor is running at the angular velocity 2.omega.n [rad/s], there hold the following equations: ##EQU2## Here, if further there hold the following relations, EQU Id.sub.1 .multidot.Kd.multidot..omega.n=Id.sub.2 .multidot.Kd.multidot.2.omega.n (7a) EQU Iq.sub.1 .multidot.Kq.multidot..omega.n=Iq.sub.2 .multidot.Kq.multidot.2.omega.n (7b)
the above equation (6) becomes as follows: EQU V.sub.2 .perspectiveto.[E.sub.1.sup.2 +2E.sub.1 (E.sub.1 +Iq.sub.2 .multidot.r+Id.sub.1 .multidot.Xd.sub.1)+V.sub.1.sup.2 ].sup.1/2( 8)
and, hence, V.sub.2 assumes a value nearly twice that of V.sub.1. Further, when the motor runs at an angular velocity 3.omega.n, the terminal voltage V.sub.3 will be about three times the terminal voltage V.sub.1, provided the conditions corresponding to the above relations (7a), (7b) hold true. For example, in a one synchronous motor, assuming the rotational speed is denoted by N(rpm), other coefficients are as follows.
E=0.09 N [volts] PA1 Xd=0.006 N [ohms] PA1 Xq=0.004 N [ohms] PA1 r=0.8 [ohms] PA1 Iq.sub.1 =4 [amps] PA1 Id.sub.1 =3 [amps]
In the case of the conditions above, further the value of N is given as 1,000 [rpm] the equation (5) is as follows: ##EQU3## Then, the value of N is given as 2,000 [rpm] and when the following equations hold true: EQU Iq.sub.1 .multidot.Xq.sub.1 =Iq.sub.2 .multidot.Xq.sub.2 EQU Id.sub.1 .multidot.Xd.sub.1 =Id.sub.2 .multidot.Xd.sub.2
The value of V.sub.2 corresponding to equation (6) is as follows. ##EQU4## Therefore, the value of V.sub.2 nearly equals to twice of the value of V.sub.1.
Thus, when the power factor is lagging, when the torque angle .delta. is smaller than the power-factor angle .phi. and when the vector diagram of voltage and current is as shown in FIG. 1, it is necessary to apply a voltage greater than the terminal voltage which is applied when the motor is operated at the rated speed, if it is attempted to run the synchronous motor at a speed faster than the rated speed.
In recent years, a semiconductor power inverter has been frequently employed as a variable-frequency power supply for varying the speed of the motor. In this case, however, the upper limit of the power-supply voltage is limited by the voltage characteristics of the semiconductor element. This often determines the upper limit of the variable-speed operation when a predetermined output is required. Therefore, if it is attempted to run the synchronous motor over a wide range of speed, the rated voltage must be set to a low value. Consequently, the synchronous motor tends to become of the type which runs at a low voltage and on a heavy current. In other words, it becomes difficult to design and manufacture the machine.
The problem of the synchronous motor can be solved if the rated voltage is set to a large value. However, the maximum voltage the semiconductor elements forming the power supply can withstand imposes the upper limit on the power-supply voltage, which then imposes a limitation on the range for varying the speed of the synchronous motor. This is the defect inherent in the conventional system for controlling synchronous motors.